I agree, get some dumbbells and weights to supplement your pushups. Especially the ones where you can adjust the weight if you intend to build. You'll also benefit from a bench for presses and ab exercises. There's a lot you can do with super basic equipment...

My first trainer walked me into the gym and said , "'All of the machines you see here are for selling memberships , get down on the mat." I learned how to get fit from him and it was all stuff you could do at home . Check out the jump rope exercises on here. Guess what you don't even need a jump rope!